((x+8)*(x+8))-100=0

Solution for ((x+8)*(x+8))-100=0 equation:

((x+8)(x+8))-100=0

We multiply parentheses ..

((+x^2+8x+8x+64))-100=0


We calculate terms in parentheses: +((+x^2+8x+8x+64)), so:

(+x^2+8x+8x+64)

We get rid of parentheses

x^2+8x+8x+64

We add all the numbers together, and all the variables

x^2+16x+64

Back to the equation:

+(x^2+16x+64)


We get rid of parentheses

x^2+16x+64-100=0

We add all the numbers together, and all the variables

x^2+16x-36=0

a = 1; b = 16; c = -36;
Δ = b2-4ac
Δ = 162-4·1·(-36)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-20}{2*1}=\frac{-36}{2}
=-18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+20}{2*1}=\frac{4}{2}
=2
$